One-loop calculations in quantumgravity: graviton self-energy, perturbative gauge invariance and Slavnov-Wardidentities

Abstract

In this paper we calculate the one-loop graviton self-energy within theframework of causal perturbation theory. Because of thisregularization/renormalization scheme, the result is ultraviolet finite,without introducing counterterms, and cut-off-free. In addition, it satisfiesthe gravitational Slavnov-Ward identities for the two-point connectedGreen function. The latter are also investigated from the point of viewof a perturbative formulation of operator gauge invariance. Then, thecondition of perturbative gauge invariance to second order for loop graphsis proved. Corrections to the Newtonian potential coming from thegraviton self-energy are also derived.